ГДЗ по алгебре 8 класс Мерзляк Задание 186

\[\boxed{\text{186\ (186).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\frac{a^{\backslash a + 1} - \frac{a^{2}}{a + 1}}{a^{\backslash a + 1} - \frac{a}{a + 1}} =\]

\[= \frac{\frac{a(a + 1) - a^{2}}{a + 1}}{\frac{a(a + 1) - a}{a + 1}} =\]

\[= \frac{\frac{a^{2} + a - a^{2}}{a + 1}}{\frac{a^{2} + a - a}{a + 1}} =\]

\[= \frac{a}{a + 1}\ :\frac{a^{2}}{a + 1} =\]

=\(\frac{a(a + 1)}{(a + 1) \cdot a^{2}} = \frac{1}{a}\)

\[2)\ \frac{a^{\backslash a} - \frac{6a - 9}{a}}{1^{\backslash a} - \frac{3}{a}} = \frac{\frac{a^{2} - 6a + 9}{a}}{\frac{a - 3}{a}} =\]

\[= \frac{(a - 3)^{2}}{a}\ :\frac{a - 3}{a} =\]

\[= \frac{(a - 3)^{2} \cdot a}{a(a - 3)} =\]

\[a - 3\]

\[3)\ \frac{1}{1 - \frac{1}{1^{\backslash a} + \frac{1}{a}}} =\]

\[= 1\ :\left( 1 - \frac{1}{\frac{a + 1}{a}} \right) =\]

\[= 1\ :\left( 1^{\backslash a + 1} - \frac{a}{a + 1} \right) =\]

\[= 1\ :\frac{a + 1 - a}{a + 1} =\]

\[= 1\ :\frac{1}{a + 1} = a + 1\]

\[4)\ \frac{\frac{2a - b}{b} + 1^{\backslash b}}{\frac{2a + b}{b} - 1^{\backslash b}} + \frac{3^{\backslash a} - \frac{b}{a}}{\frac{3a}{b} - 1^{\backslash b}} =\]

\[= \frac{\frac{2a - b + b}{b}}{\frac{2a + b - b}{b}} + \frac{\frac{3a - b}{a}}{\frac{3a - b}{b}} =\]

\[= \frac{2a}{b}\ :\frac{2a}{b} + \frac{3a - b}{a}\ :\frac{3a - b}{b} =\]

\[= 1 + \frac{3a - b}{a} \cdot \frac{b}{3a - b} =\]

\[= 1^{\backslash a} + \frac{b}{a} = \frac{a + b}{a}\]